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\Veierstrass on the other hand believed that he had at last made
the square root of 2 as comprehensible and as safe to handle as
2 itself; Kronecker denied that the square root of 2 'exists', and
he asserted that it is impossible to reason consistently with or
about the Weierstrassian construction for this root or for any
other irrational. Neither his older colleagues nor the young to
whom Kronecker addressed himself gave his revolutionary idea
a very enthusiastic welcome,
\Yeierstrass himself seems to have felt uneasy: certainly he
was hurt. His strong emotion is released mostly in one tre-
mendous German sentence* like a fugue, which it is almost
impossible to preserve in English. 'But the worst of it is', lie
complains, 'that Kronecker uses his authority to proclaim that
all those who up to new have laboured to establish the theory
of functions are sinners before the Lord. When a whimsical
eccentric like ChristofTei [the man whose somewhat neglected
•work was to become, years after liis death, an important tool in
differential geometry as it is cultivated to-day in the mathe-
matics of relativity] says that in twenty or thirty years the
present theory of functions will be buried and that the whole of
analysis will be referred to the theory of forms, we reply with
a shrug. But when Kronecker delivers himself of the following
verdict which I repeat word for teord: 4klf time and strength are
granted me, I myself will show the mathematical world that not
only geometry, but also arithmetic can point the way to
analysis, and certainly a more rigorous way. If I cannot do it
myself those who come after me will... and they will recognize
the incorrectness of all those conclusions with which so-called
analysis works at present" - such a verdict from a man whose
emiEsent talent and distinguished performance in mathematical
research I admire as sincerely and with as much pleasure as all
iiis colleagues, is not only humiliating for those whom he adjures
to acknowledge as an error and to forswear the substance of
what has constituted the object of then: thought and unremit-
ting labour, but it is a direct appeal to the younger generation
to desert then- present leaders and rally around him as the
disciple of a new system which must be founded. Truly it is sad,
In a letter to Sonja KowalewsM, 1885.